Four-neutrino oscillation solutions of the solar neutrino problem

We present an analysis of the neutrino oscillation solutions of the solar neutrino problem in the framework of four-neutrino mixing where a sterile neutrino is added to the three standard ones. We perform a fit to the full data set corresponding to the 825-day Super-Kamiokande data sample as well as to chlorine, GALLEX, and SAGE and Kamiokande experiments. In our analysis we use all measured total event rates as well as all Super-Kamiokande data on the zenith angle dependence and the recoil electron energy spectrum. We consider both transitions via the Mikheyev-Smirnov-Wolfenstein (MSW) mechanism as well as oscillations in vacuum (just-so) and find the allowed solutions for different values of the additional mixing angles. This framework permits transitions into active or sterile neutrinos controlled by the additional parameter ${\cos }^2\left({\vartheta }_{23}\right){\cos }^2\left({\vartheta }_{24}\right)$ and contains as limiting cases the pure ${\nu }_e$-active and ${\nu }_e$-sterile neutrino oscillations. We discuss the maximum allowed values of this additional mixing parameter for the different solutions. As a particularity, we also show that for MSW transitions there are solutions at 99% C.L. at ${\vartheta }_{12}$ mixing angles greater than $\pi /4\mathrm{}$ and that the best-fit point for the zenith angle distribution is in the second octant.